Autonomous experimentation is an emerging area of research, primarily related to autonomous vehicles, scientific combinatorial discovery approaches in materials science and drug discovery, and iterative research loops of planning, experimentation, and analysis. However, autonomous approaches developed in these contexts are difficult to apply to high-dimensional mapping technologies, such as scanning hyperspectral imaging of biological systems, due to sample complexity and heterogeneity. We briefly cover the history of adaptive sampling algorithms and surrogate modeling in order to define autonomous adaptive data acquisition as an objective-based, flexible building block for future biological imaging experimentation driven by intelligent infrastructure. We subsequently summarize the recent implementations of autonomous adaptive data acquisition (AADA) for scanning hyperspectral imaging, assess how these address the difficulties of autonomous approaches in hyperspectral imaging, and highlight the AADA design variation from a goal-oriented perspective. Finally, we present a modular AADA architecture that embeds AADA-driven flexible building blocks to address the challenge of time resolution for high-dimensional scanning hyperspectral imaging of nonequilibrium dynamical systems. In our example research-driven experimental design case, we propose an AADA infrastructure for time-resolved, noninvasive, and label-free scanning hyperspectral imaging of living biological systems. This AADA infrastructure can accurately target the correct state of the system for experimental workflows that utilize subsequent expensive, high-information-content analytical techniques.